Abstract

In this paper we introduce a family of densities based on a new type of expansions that we name General Moments Expansions. We argue that our approach presents theoretical advantages over Edgeworth and Charlier type of expansions, which are related to, on the one hand, the simplicity of their polynomials (i.e. the orthogonality property is not required yet), and on the other hand, their generality, since they can easily be applied to any distribution with finite moments up to the polynomial truncation order. We illustrate the usefulness of the proposed densities through an out-of-sample forecasting exercise for exchange-rate returns risk. Our results show that the proposed model provides fairly accurate volatility and VaR forecasts in comparison the ones obtained from the VaR procedure proposed in Engle (2001) and a GARCH model with Student's t errors.